Instructions. Read each problem carefully. For datasets, sort values before computing measures of center or spread. For stem-and-leaf plots, leaves should always increase as you move away from the stem. Round means to the nearest whole number where indicated. Select one answer per question.
A teacher recorded the number of text messages two students sent each day for one week. What is the IQR for each student?
| Student A — Week 1 | Student B — Week 2 |
|---|
| 32 45 28 51 38 47 41 |
25 50 33 42 30 48 36 |
- The IQR for Week 1 is 15, and the IQR for Week 2 is 18.
- The IQR for Week 1 is 23, and the IQR for Week 2 is 25.
- The IQR for Week 1 is 18, and the IQR for Week 2 is 15.
- The IQR for Week 1 is 41, and the IQR for Week 2 is 36.
The stem-and-leaf plot shows the number of minutes boys and girls spent exercising on Saturday. What is the mean for each group, rounded to the nearest whole number?
| Boys | Stem | Girls |
|---|
| 8 | 1 | 5 |
| 5 2 | 2 | 0 8 |
| 8 3 1 | 3 | 0 2 5 |
| 2 | 4 | 0 |
Key: 8 | 1 | 5 = 18 and 15
- The mean for boys is 29 and the mean for girls is 30.
- The mean for boys is 30 and the mean for girls is 29.
- The mean for boys is 31 and the mean for girls is 30.
- The mean for boys is 209 and the mean for girls is 200.
Which back-to-back stem-and-leaf plot correctly represents the data sets shown below?
| Set A | Set B |
|---|
| 24 31 35 38 42 48 |
19 27 33 36 41 45 |
A
| Set A | Stem | Set B |
|---|
| | 1 | 9 |
| 4 | 2 | 7 |
| 8 5 1 | 3 | 3 6 |
| 8 2 | 4 | 1 5 |
B
| Set A | Stem | Set B |
|---|
| 9 | 1 | |
| 7 | 2 | 4 |
| 6 3 | 3 | 1 5 8 |
| 5 1 | 4 | 2 8 |
C
| Set A | Stem | Set B |
|---|
| | 1 | 9 |
| 4 | 2 | 7 |
| 1 5 8 | 3 | 3 6 |
| 2 8 | 4 | 1 5 |
D
| Set A | Stem | Set B |
|---|
| | 1 | 9 |
| 4 | 2 | 7 |
| 8 5 1 | 3 | 6 3 |
| 8 2 | 4 | 5 1 |
A weather station recorded daily rainfall (in millimeters) for one week in two different months. What is the IQR for each month?
| Month 1 | Month 2 |
|---|
| 12 8 15 22 9 18 14 |
16 10 20 25 13 22 11 |
- The IQR for Month 1 is 14, and the IQR for Month 2 is 15.
- The IQR for Month 1 is 9, and the IQR for Month 2 is 11.
- The IQR for Month 1 is 14, and the IQR for Month 2 is 16.
- The IQR for Month 1 is 11, and the IQR for Month 2 is 9.
The stem-and-leaf plot shows the number of pages members of two book clubs read last week. What is the mean for each group, rounded to the nearest whole number?
| Group X | Stem | Group Y |
|---|
| 5 | 2 | 8 |
| 5 2 | 3 | 0 8 |
| 7 1 | 4 | 2 9 |
| 3 | 5 | 5 |
Key: 5 | 2 | 8 = 25 and 28
- The mean for Group X is 38 and the mean for Group Y is 40.
- The mean for Group X is 40 and the mean for Group Y is 39.
- The mean for Group X is 39 and the mean for Group Y is 40.
- The mean for Group X is 39 and the mean for Group Y is 41.
Which back-to-back stem-and-leaf plot correctly represents the data sets shown below?
| Set A | Set B |
|---|
| 23 28 31 35 39 44 |
19 24 32 38 41 45 |
A
| Set A | Stem | Set B |
|---|
| | 1 | 9 |
| 8 3 | 2 | 4 |
| 5 1 | 3 | 2 8 |
| 4 | 4 | 1 5 |
B
| Set A | Stem | Set B |
|---|
| | 1 | 9 |
| 3 8 | 2 | 4 |
| 1 5 9 | 3 | 2 8 |
| 4 | 4 | 1 5 |
C
| Set A | Stem | Set B |
|---|
| 9 | 1 | |
| 4 | 2 | 3 8 |
| 8 2 | 3 | 1 5 9 |
| 5 1 | 4 | 4 |
D
| Set A | Stem | Set B |
|---|
| | 1 | 9 |
| 8 3 | 2 | 4 |
| 9 5 1 | 3 | 2 8 |
| 4 | 4 | 1 5 |
A consumer report measured customer wait times (in minutes) at two restaurants over one week. What is the IQR for each restaurant?
| Restaurant A | Restaurant B |
|---|
| 20 15 25 28 22 18 30 |
24 18 28 35 20 32 12 |
- The IQR for Restaurant A is 15, and the IQR for Restaurant B is 23.
- The IQR for Restaurant A is 22, and the IQR for Restaurant B is 24.
- The IQR for Restaurant A is 10, and the IQR for Restaurant B is 14.
- The IQR for Restaurant A is 14, and the IQR for Restaurant B is 10.
The stem-and-leaf plot shows the test scores for two seventh-grade classes. What is the mean score for each class, rounded to the nearest whole number?
| Class A | Stem | Class B |
|---|
| 5 | 6 | |
| 5 0 | 7 | 2 8 |
| 8 4 0 | 8 | 2 5 8 |
| 0 | 9 | 2 5 |
Key: 5 | 6 | 2 = 65 and 62 (no value of 62 in this set)
- The mean for Class A is 80 and the mean for Class B is 85.
- The mean for Class A is 79 and the mean for Class B is 85.
- The mean for Class A is 85 and the mean for Class B is 79.
- The mean for Class A is 79 and the mean for Class B is 84.
Which back-to-back stem-and-leaf plot correctly represents the data sets shown below?
| Set A | Set B |
|---|
| 47 52 58 63 65 71 |
41 49 55 60 68 73 |
A
| Set A | Stem | Set B |
|---|
| 7 | 4 | 1 |
| 8 2 | 5 | 5 |
| 5 3 | 6 | 0 8 |
| 1 | 7 | 3 |
B
| Set A | Stem | Set B |
|---|
| 7 | 4 | 9 1 |
| 8 2 | 5 | 5 |
| 5 3 | 6 | 8 0 |
| 1 | 7 | 3 |
C
| Set A | Stem | Set B |
|---|
| 9 1 | 4 | 7 |
| 5 | 5 | 2 8 |
| 8 0 | 6 | 3 5 |
| 3 | 7 | 1 |
D
| Set A | Stem | Set B |
|---|
| 7 | 4 | 1 9 |
| 8 2 | 5 | 5 |
| 5 3 | 6 | 0 8 |
| 1 | 7 | 3 |
A researcher recorded the number of phone calls made per day by an adult and a teenager over one week. What is the IQR for each person?
| Adult | Teenager |
|---|
| 8 5 12 3 9 7 15 |
2 11 4 18 6 13 8 |
- The IQR for the adult is 12, and the IQR for the teenager is 16.
- The IQR for the adult is 8, and the IQR for the teenager is 8.
- The IQR for the adult is 7, and the IQR for the teenager is 9.
- The IQR for the adult is 9, and the IQR for the teenager is 7.
Answer Key
Verify your work against the table below. Each correct answer is the result of the standard procedure for that question type (sort → identify quartiles for IQR; extract values → sum and divide for mean; align leaves outward from the stem for construction).
| Question | Topic | Answer |
|---|
| Q1 | IQR Comparison | A |
| Q2 | Stem-and-Leaf Mean | B |
| Q3 | Stem-and-Leaf Construction | A |
| Q4 | IQR Comparison | B |
| Q5 | Stem-and-Leaf Mean | C |
| Q6 | Stem-and-Leaf Construction | D |
| Q7 | IQR Comparison | C |
| Q8 | Stem-and-Leaf Mean | B |
| Q9 | Stem-and-Leaf Construction | D |
| Q10 | IQR Comparison | C |